Write an inequality that represents each situation. graph the solution. Help appreaciated Thanks.
4x + 6 ¡Ý 34.
Sorry, your ¡Ý symbol doesn't make sense. What were you trying to type? Greater than or equal?
Whatever the symbol is, I suggest subtracting 6 from both sides of the inequality and then dividing both sides by 4. The direction of the > or < sign will stay the same.
write an inequality that represents each situation. Graph the solution
4x + 6 ¡Ý 34.
To write an inequality that represents the situation, "4x + 6 ≥ 34," we use the greater than or equal to symbol (≥) because we want to include the value of 34:
The inequality is: 4x + 6 ≥ 34.
To graph the solution, we need to plot the points on a number line. To do this, we can start by isolating the variable x:
4x + 6 ≥ 34
Subtract 6 from both sides to isolate the term with the variable:
4x ≥ 28
Now, divide both sides by 4 to solve for x:
x ≥ 7
So, the solution is x is greater than or equal to 7.
On a number line, represent this by drawing a closed circle on 7 and shading to the right:
---●==================
7
The shaded part represents all the values of x that satisfy the inequality 4x + 6 ≥ 34, which are x ≥ 7.
To write an inequality that represents the situation, we can follow these steps:
Step 1: Identify the variable: In this case, the variable is x.
Step 2: Translate the given information into mathematical terms: The inequality states that "4x + 6 is greater than or equal to 34."
Step 3: Write down the inequality: Based on the information given, we can write the inequality as follows: 4x + 6 ≥ 34.
Now, to graph the solution, we need to represent the possible values of x that satisfy the inequality. Here's how to do it:
Step 4: Isolate the variable: To solve for x, we need to isolate it on one side of the inequality. Start by subtracting 6 from both sides:
4x + 6 - 6 ≥ 34 - 6
4x ≥ 28
Step 5: Divide by the coefficient of x: Since 4 is multiplying x, we can divide both sides of the inequality by 4:
(4x)/4 ≥ 28/4
x ≥ 7
Step 6: Represent the solution on a number line: To graph the solution, draw a number line and mark a point at 7. Since the inequality states that x is greater than or equal to 7, put a closed dot (•) on the mark for 7.
Step 7: Indicate the solution region: Since the inequality is "greater than or equal to," shade the region to the right of the closed dot, including the dot itself. This indicates all the values of x that make the inequality true.
So, on the number line, shade the region to the right of the closed dot at 7, and that represents the solution to the inequality.